Or, think about it another way.

A general computer is built from (in a simplified picture) a set of 2-state
transistors, on or off, the celebrated 0 or 1 bits. The integrated circuits
of cpu's are now consistently on the order of greater than 1 billion
(1*10^9) transistors.

Human DNA is consistently of order 3 billion base pairs, and base pairs are
also a 2-bit system, coming in two types (A-T or C-G), so 0 or 1.

Here's one key difference. We know how the circuits of a computer are
integrated, because we built and designed them.

We're only just learning how the circuits, or transistors, of DNA are
integrated.

And here's one very simple picture of how this learning is going to complicate
the idea of DNA as computer. A transistor doesn't have to be just a 0 or 1,
a switch. A transistor can also be an amplifier.

Genes aren't read-once, copy forever. How they are read differs depending on
the thermodynamic state in which they are read. Salt concentration, cell
crowding, cell aging, each of these and unknown variables change the result
of reading a gene over time. Thus, at the most extreme, cancer. But also
mutations, different cell types from the same genes, etc.

In other words, take all the wonderful incredible things that a computer can
do, and realize that DNA is significantly more complicated. We have a long
way to go to reverse engineer the circuitry of DNA, and even when we do, it
will only be the beginning, because it's a dynamically modifiable system.

Or to put it another away, whenever someone talks about the information content
of DNA, that's only the most basic, digital approximation. Chemistry is both
digital, and analogue.